A Convex Optimization Approach for Source Localization using LBI Changing Rate of Phase Difference Only

We target the source localization problem using only changing rate of phase difference (CRPD) measurements collected by a moving platform with a long baseline interferometer. Source localization using CRPD measurements is a non-convex problem requiring advanced techniques to be resolved. In our paper, we first form a constrained-weighted least squares (CWLS) problem from the maximum-likelihood (ML) function. Then, we transform the CWLS problem into a semi-definite programming. By dropping the rank-one constraint, we achieve semi-definite relaxation, and the problem becomes convex, which interior-point algorithms can optimally solve. In the simulations, we compare the proposed method to the pseudo-linear approaches, ML solver, and Cramer-Rao lower bound (CRLB). We observe that the proposed method attains the CRLB at low noise levels and outperforms the pseudo-linear approaches while performing similarly to the ML solver.